We present IRAM Plateau de Bure interferometric detections of CO(J = 1 → 0) emission from a 24 μm-selected sample of star-forming galaxies at z = 0.4. The galaxies have polycyclic aromatic hydrocarbon 7.7 μm-derived star formation rates of SFR ∼30-60 M⊙ yr-1 and stellar masses M* 1011 M. The CO(J = 1 → 0) luminosities of the galaxies imply that the disks still contain a large reservoir of molecular gas, contributing ∼20% of the baryonic mass, but have star formation "efficiencies" similar to local quiescent disks and gas-dominated disks at z ∼ 1.5-2. We reveal evidence that the average molecular gas fraction has undergone strong evolution since z ∼ 2, with f gas (1 + z)∼2±0.5. The evolution of f gas encodes fundamental information about the relative depletion/replenishment of molecular fuel in galaxies and is expected to be a strong function of halo mass. We show that the latest predictions for the evolution of the molecular gas fraction in semi-analytic models of galaxy formation within a ΛCDM universe are supported by these new observations. © 2011. The American Astronomical Society. All rights reserved.